Clapeyron Neural Networks for Single-Species Vapor-Liquid Equilibria

TL;DR

This work addresses single-species vapor–liquid equilibria by combining a graph neural network with thermodynamics-informed learning. By training a multi-task GNN to predict $p^{sat}(T)$, $V^{V}(T)$, $V^{L}(T)$, and $\Delta H_{V}(T)$ and incorporating the Clapeyron relation as a soft regularization term, the method achieves high predictive accuracy while substantially improving adherence to thermodynamic consistency. The Clapeyron-GNN outperforms purely data-driven baselines in consistency (lower Clapeyron error) and, in many cases, matches or exceeds predictive performance, especially for data-scarce properties. This approach is particularly valuable for data-scarce scenarios in chemical engineering, enabling more reliable VLE predictions from molecular structure and temperature alone, with potential for hard-constraint extensions in future work.

Abstract

Machine learning (ML) approaches have shown promising results for predicting molecular properties relevant for chemical process design. However, they are often limited by scarce experimental property data and lack thermodynamic consistency. As such, thermodynamics-informed ML, i.e., incorporating thermodynamic relations into the loss function as regularization term for training, has been proposed. We herein transfer the concept of thermodynamics-informed graph neural networks (GNNs) from the Gibbs-Duhem to the Clapeyron equation, predicting several pure component properties in a multi-task manner, namely: vapor pressure, liquid molar volume, vapor molar volume and enthalpy of vaporization. We find improved prediction accuracy of the Clapeyron-GNN compared to the single-task learning setting, and improved approximation of the Clapeyron equation compared to the purely data-driven multi-task learning setting. In fact, we observe the largest improvement in prediction accuracy for the properties with the lowest availability of data, making our model promising for practical application in data scarce scenarios of chemical engineering practice.

Figures (4)

• Figure 1: Schematic illustration of Clapeyron-GNN
• Figure 2: Histograms of data distributions for four target properties and 40 bins for numeric values across all properties
• Figure 3: Parity plots of test set MTL-GNN and Clapeyron-GNN
• Figure 4: p(V)-plots and $\Delta$H$_{\text{v}}$(T)-plots for four exemplary molecules of the test set: experimental data in black crosses, multi-task learning in blue dots, Clapeyron-informed learning with LeakyReLU in green dots, and Clapeyron-informed learning with SiLU in orange triangles.